A New Jacobi Elliptic Function Expansion Method for Solvinga Nonlinear PDE Describing Pulse Narrowing Nonlinear Transmission Lines

Elsayed M. E. Zayed; K. A. E. Alurrfi

doi:10.4208/jpde.v28.n2.3

Authors

Elsayed M. E. Zayed Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, Egypt
K. A. E. Alurrfi Department of Mathematics, Faculty of Science, Zagazig University, P. O. Box 44519, Zagazig, Egypt

DOI:

https://doi.org/10.4208/jpde.v28.n2.3

Keywords:

New Jacobi elliptic function expansion method;pulse narrowing nonlinear transmission lines;exact solutions;Kirchhoff's current law;Kirchhoff's voltage law

Abstract

" In this article, we apply the first elliptic function equation to find a new kind of solutions of nonlinear partial differential equations (PDEs) based on the homogeneous balance method, the Jacobi elliptic expansion method and the auxiliary equation method. New exact solutions to the Jacobi elliptic functions of a nonlinear PDE describing pulse narrowing nonlinear transmission lines are given with the aid of computer program, e.g. Maple or Mathematica. Based on Kirchhoff's current law and Kirchhoff's voltage law, the given nonlinear PDE has been derived and can be reduced to a nonlinear ordinary differential equation (ODE) using a simple transformation. The given method in this article is straightforward and concise, and can be applied to other nonlinear PDEs in mathematical physics. Further results may be obtained."